I would still do the same as the rest of the house.

To choose between a handle or a knob for your 15-pane door, it mainly depends on your personal preferences and the overall style of your home. Since you already have Venetian bronze door knobs with square roses throughout your house, it might be better to stay consistent with the same design. However, if you want to bring a different touch to the family room, you could opt for a handle with the same square rose, which would create an aesthetic connection while offering a slightly different look.

In any case, it's essential to choose a style that you like and that fits harmoniously into the overall aesthetics of your home. Since the other doors are not within the sightline of this one, it leaves some flexibility to choose between a knob or a handle without disrupting the overall design.